The orthogonal trajectories of the first tangents of the curve are called the involutes of x. The hyperspheres which have higher order contact with a curve x are known osculating hyperspheres of x. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve x in n-dimensional Euclidean space E-n. In the present study, we give a characterization of involute curves of order k (resp. evolute curves) of the given curve x in n-dimensional Euclidean space E-n. Further, we obtain some results on these type of curves in E-3 and E-4, respectively.
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Kadri ARSLAN
Betül BULCA
Gunay Őzturk
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ARSLAN et al. (Thu,) studied this question.
synapsesocial.com/papers/69a3d6eaec16d51705d2d95e — DOI: https://doi.org/10.5666/kmj.2018.58.1.117